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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.linear;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    /**<a name="line.21"></a>
<FONT color="green">022</FONT>     * An interface to classes that implement an algorithm to calculate the<a name="line.22"></a>
<FONT color="green">023</FONT>     * LU-decomposition of a real matrix.<a name="line.23"></a>
<FONT color="green">024</FONT>     * &lt;p&gt;The LU-decomposition of matrix A is a set of three matrices: P, L and U<a name="line.24"></a>
<FONT color="green">025</FONT>     * such that P&amp;times;A = L&amp;times;U. P is a rows permutation matrix that is used<a name="line.25"></a>
<FONT color="green">026</FONT>     * to rearrange the rows of A before so that it can be decomposed. L is a lower<a name="line.26"></a>
<FONT color="green">027</FONT>     * triangular matrix with unit diagonal terms and U is an upper triangular matrix.&lt;/p&gt;<a name="line.27"></a>
<FONT color="green">028</FONT>     * &lt;p&gt;This interface is based on the class with similar name from the<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;a href="http://math.nist.gov/javanumerics/jama/"&gt;JAMA&lt;/a&gt; library.&lt;/p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * &lt;ul&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     *   &lt;li&gt;a {@link #getP() getP} method has been added,&lt;/li&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     *   &lt;li&gt;the &lt;code&gt;det&lt;/code&gt; method has been renamed as {@link #getDeterminant()<a name="line.32"></a>
<FONT color="green">033</FONT>     *   getDeterminant},&lt;/li&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     *   &lt;li&gt;the &lt;code&gt;getDoublePivot&lt;/code&gt; method has been removed (but the int based<a name="line.34"></a>
<FONT color="green">035</FONT>     *   {@link #getPivot() getPivot} method has been kept),&lt;/li&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     *   &lt;li&gt;the &lt;code&gt;solve&lt;/code&gt; and &lt;code&gt;isNonSingular&lt;/code&gt; methods have been replaced<a name="line.36"></a>
<FONT color="green">037</FONT>     *   by a {@link #getSolver() getSolver} method and the equivalent methods provided by<a name="line.37"></a>
<FONT color="green">038</FONT>     *   the returned {@link DecompositionSolver}.&lt;/li&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;/ul&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     *<a name="line.40"></a>
<FONT color="green">041</FONT>     * @see &lt;a href="http://mathworld.wolfram.com/LUDecomposition.html"&gt;MathWorld&lt;/a&gt;<a name="line.41"></a>
<FONT color="green">042</FONT>     * @see &lt;a href="http://en.wikipedia.org/wiki/LU_decomposition"&gt;Wikipedia&lt;/a&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>     * @version $Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $<a name="line.43"></a>
<FONT color="green">044</FONT>     * @since 2.0<a name="line.44"></a>
<FONT color="green">045</FONT>     */<a name="line.45"></a>
<FONT color="green">046</FONT>    public interface LUDecomposition {<a name="line.46"></a>
<FONT color="green">047</FONT>    <a name="line.47"></a>
<FONT color="green">048</FONT>        /**<a name="line.48"></a>
<FONT color="green">049</FONT>         * Returns the matrix L of the decomposition.<a name="line.49"></a>
<FONT color="green">050</FONT>         * &lt;p&gt;L is an lower-triangular matrix&lt;/p&gt;<a name="line.50"></a>
<FONT color="green">051</FONT>         * @return the L matrix (or null if decomposed matrix is singular)<a name="line.51"></a>
<FONT color="green">052</FONT>         */<a name="line.52"></a>
<FONT color="green">053</FONT>        RealMatrix getL();<a name="line.53"></a>
<FONT color="green">054</FONT>    <a name="line.54"></a>
<FONT color="green">055</FONT>        /**<a name="line.55"></a>
<FONT color="green">056</FONT>         * Returns the matrix U of the decomposition.<a name="line.56"></a>
<FONT color="green">057</FONT>         * &lt;p&gt;U is an upper-triangular matrix&lt;/p&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>         * @return the U matrix (or null if decomposed matrix is singular)<a name="line.58"></a>
<FONT color="green">059</FONT>         */<a name="line.59"></a>
<FONT color="green">060</FONT>        RealMatrix getU();<a name="line.60"></a>
<FONT color="green">061</FONT>    <a name="line.61"></a>
<FONT color="green">062</FONT>        /**<a name="line.62"></a>
<FONT color="green">063</FONT>         * Returns the P rows permutation matrix.<a name="line.63"></a>
<FONT color="green">064</FONT>         * &lt;p&gt;P is a sparse matrix with exactly one element set to 1.0 in<a name="line.64"></a>
<FONT color="green">065</FONT>         * each row and each column, all other elements being set to 0.0.&lt;/p&gt;<a name="line.65"></a>
<FONT color="green">066</FONT>         * &lt;p&gt;The positions of the 1 elements are given by the {@link #getPivot()<a name="line.66"></a>
<FONT color="green">067</FONT>         * pivot permutation vector}.&lt;/p&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>         * @return the P rows permutation matrix (or null if decomposed matrix is singular)<a name="line.68"></a>
<FONT color="green">069</FONT>         * @see #getPivot()<a name="line.69"></a>
<FONT color="green">070</FONT>         */<a name="line.70"></a>
<FONT color="green">071</FONT>        RealMatrix getP();<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>        /**<a name="line.73"></a>
<FONT color="green">074</FONT>         * Returns the pivot permutation vector.<a name="line.74"></a>
<FONT color="green">075</FONT>         * @return the pivot permutation vector<a name="line.75"></a>
<FONT color="green">076</FONT>         * @see #getP()<a name="line.76"></a>
<FONT color="green">077</FONT>         */<a name="line.77"></a>
<FONT color="green">078</FONT>        int[] getPivot();<a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>        /**<a name="line.80"></a>
<FONT color="green">081</FONT>         * Return the determinant of the matrix<a name="line.81"></a>
<FONT color="green">082</FONT>         * @return determinant of the matrix<a name="line.82"></a>
<FONT color="green">083</FONT>         */<a name="line.83"></a>
<FONT color="green">084</FONT>        double getDeterminant();<a name="line.84"></a>
<FONT color="green">085</FONT>    <a name="line.85"></a>
<FONT color="green">086</FONT>        /**<a name="line.86"></a>
<FONT color="green">087</FONT>         * Get a solver for finding the A &amp;times; X = B solution in exact linear sense.<a name="line.87"></a>
<FONT color="green">088</FONT>         * @return a solver<a name="line.88"></a>
<FONT color="green">089</FONT>         */<a name="line.89"></a>
<FONT color="green">090</FONT>        DecompositionSolver getSolver();<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>    }<a name="line.92"></a>




























































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